1. Field of the Invention
This invention relates generally to run-length-limited (RLL) codes permitting high-density recording in optical and magnetic storage media and, more specifically, to a system for transforming between a high rate 2 M/N asymmetric RLL code and a rate M/N evenspaced RLL code suitable for use with magnetic and magneto-optical recording.
2. Description of the Related Art
In many digital magnetic recording systems, digital data is represented by flux transitions positioned within discrete time intervals between either of two possible states of magnetization in a recording medium. It is convenient to represent patterns of such flux transitions as binary sequences in which the presence or absence of a transition within a code symbol clock interval is indicated by a first or second code symbol such as "1" or "0", respectively. The physical necessity of limiting the minimum and maximum spacing between flux transitions in the medium is expressed in the two run-length constraints (d, k) on the binary sequences, which respectively designate the minimum and maximum number of second code symbols "0") occurring between successive first codes symbols ("0"). A set of rules for mapping M arbitrary user data bit sequences into N bits of a constrained code sequence is herein denominated a run-length-limited (RLL) code of rate M/N.
Even-spaced RLL codes having an even-consecutive-zero constraint in addition to the usual (d, k) run length constraints were first proposed by Paul Funk ("Run-Length-Limited Codes with Multiple Spacing", IEEE Trans. Magnetics, Vol. Mag-18, No. 2, pp. 772-775, March 1982) and are herein denominated as (d, k, 2) or (2d, 2k, 2) RLL codes. Funk observed that multiple-spaced codes are disadvantaged by the potentially infinite propagation of symbol detection errors but showed for the special case of even-spacing that this infinite detection-error propagation can be eliminated through the use of a transition-polarity detection scheme. Also, in U.S. Pat. No. 4,928,187, Rees describes a rate 1/3 (2, 8, 2) RLL code with features similar to those of the 1/3 rate (2, 8, 2) RLL code discussed by Funk.
D. Rugar et al. ("Recording Results and Coding Considerations for the Resonant Biased Coil Overwrite Technique", Proc. of the Optical Data Storage Topical Meeting in Los Angeles, 1989, SPIE Vol. 1078, pp. 265-270) explore Funk's even-spaced RLL codes for particular application to resonant biased-coil magneto-optical recording techniques. They discuss using rate 1/3 (2, 6, 2) and rate 2/5 (2, 18, 2) even-spaced RLL codes for resonant coil overwriting in magneto-optical data recorders.
The rate 2/5 (2, 18, 2) RLL code was found to be superior to the rate 2/3(1, 7), rate 1/2 (2, 7), and rate 1/3 (2, 8, 2) RLL codes when used for pulse-width modulation (PWM) recording with either maximum slope or threshold detection channels and also was found to be superior to all other known RLL codes for optical partial response maximum likelihood (PRML) type data channels, including the rate 2/3 (1, 7) RLL code at linear densities above 45 kbpi. Such even-spaced codes thus appear ideal for magneto-optical applications.
In U.S. Pat. No. 5,173,694, entirely incorporated herein by this reference, R. T. Lynch, Jr. et al. disclose a practical method for encoding and decoding a rate 2/5 (2, 18, 2) RLL code. Their encoding and decoding technique was developed using the state-splitting algorithm of Adler et al. (IEEE Trans. Information Theory, Vol. IT-29, pp. 5-22, January 1983), the preliminary merging technique of Marcus et al. ("Finite-State Codes for Data Storage", IBM RJ8291, August 1991) and a "code word reassignment" technique disclosed in their patent.
Using similar code construction methods, it was later found that a rate 2/5 (2, 16, 2) even-spaced RLL code could be similarly constructed having less than 0.7 percent excess capacity without additional complexity. The maximum theoretical rate of a (2, 16, 2) code is 0.40274, so the 2/5 rate is 99.3 percent efficient. Rate 2/5(2, 16, 2) even-spaced RLL codes are well-suited for magneto-optic recording systems incorporating resonant-biased coil direct overwrite techniques and also are applicable to magnetic recording systems where RLL codes are used. The even-spaced property of the code provides a wider detection window than is available with the standard RLL codes, which ensures improved channel performance. The wider detection window affects the sliding block decoder used to recover original bit data from the recorded code symbols.
Table 1 shows the relative performance of several single-spaced and double-spaced RLL codes proposed for magneto-optic data recording, assuming an original user bit data rate of 40 MHz.
TABLE 1 __________________________________________________________________________ STORAGE CODE PARAMETERS FOR A 40 M BIT/SEC USER RATE CODE SLIDING MINIMUM SYMBOL CODE CODE CODE DECODER TRANSITION CLOCK RATE CONSTRAINT RATE WINDOW SPACING RATE EFFICIENCY __________________________________________________________________________ (2, 7) 1/2 12.5 ns 37.5 ns 80 MHz 96.7% (1, 7) 2/3 16.6 ns 33.3 ns 60 MHz 98.2% (2, 18, 2) 2/5 20.0 ns 30.0 ns 100 MHz 99.0% (2, 16, 2) 2/5 20.0 ns 30.0 ns 100 MHz 99.3% __________________________________________________________________________
Note that the even-spaced RLL codes have wider sliding decoder windows than either single-spaced RLL code. In optical recording, this wider window more than compensates for the somewhat greater inter-symbol interference (ISI). The wide window is also believed to be a favorable feature in DASD systems. Preliminary experiments show that the (2, 16, 2) even-spaced RLL code may provide up to 120 percent of the linear data storage density available from the (1, 7) RLL code.
The primary disadvantage of even-spaced RLL codes is the low code rate, which imposes a high data symbol clock frequency (e.g., 100 MHz). As user bit data rates increase, the elevated clock frequency required for the rate 2/5 (2, 16, 2) RLL code becomes a significant limitation. This limitation can be overcome through the use of higher-rate RLL coding.
Practitioners in the art have proposed higher rate RLL codes to improve linear recording density for data recorded on optical storage media. For instance, in U.S. Pat. No. 4,949,196, entirely incorporated herein by this reference, Neil R. Davie et al. disclose a method and apparatus for applying asymmetrical RLL codes to magnetic and optical data recording devices. The asymmetric RLL code is herein expressed as rate M/N (d.sub.1, k.sub.1 ; d.sub.2, k.sub.2), where N is the number of code symbols required to encode M user data bits, and where the single-spaced RLL constraint alternates between (d.sub.1, k.sub.1) and (d.sub.2, k.sub.2) at each recorded signal transition. Davie et al. disclose a rate 4/5 (0,10; 1, 11) asymmetric RLL code that is particularly useful because of the very high code rate.
There is a clearly-felt need in the art for a RLL code system that achieves the high code rates of the asymmetric RLL codes while also providing the wide sliding decoder windows and high code rate efficiencies of the even-spaced codes. The related unresolved problems and deficiencies are clearly felt in the art and are solved by this invention in the manner described below.